This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A336450 #14 Oct 06 2021 03:52:02
%S A336450 1,-3,4,9,16,25,36,49,-56,64,81,88,-104,121,144,-167,169,177,196,-203,
%T A336450 -243,-255,256,277,289,324,361,-363,373,-395,-411,441,484,529,576,676,
%U A336450 709,-719,729,784,841,961,1017,1024,-1028,1080,1089,-1091,1156,1296,1369
%N A336450 Values z of primitive solutions (x, y, z) to the Diophantine equation x^3 + y^3 + 2*z^3 = 2*5^6.
%C A336450 Terms are arranged in order of increasing absolute value (if equal, the negative number comes first).
%C A336450 Let x = a^(2*m) - (a^m)*t - t^2, y = a^(2*m) + (a^m)*t - t^2, z = t^2; then x^3 + y^3 + 2*z^3 = 2*a^(6*m). When a = 5, m = 1, t = 5*n + k(k = {1, 2, 3, 4}); (x, y, z) are primitive solutions of equation. Thus, A047201(n)^2 are terms of the sequence.
%D A336450 R. K. Guy, Unsolved Problems in Number Theory, D5.
%e A336450 (-20)^3 + 34^3 + 2*(-3)^3 = 31250, -3 is a term.
%e A336450 (-11)^3 + 29^3 + 2*16^3 = 15^3 + 27^3 + 2*16^3 = 31250, 16 is a term.
%t A336450 Clear[t]
%t A336450 t = {};
%t A336450 Do[y = (31250 - x^3 - 2z^3)^(1/3) /. (-1)^(1/3) -> -1;
%t A336450 If[IntegerQ[y] && GCD[x, y, z] == 1, AppendTo[t, z]], {z, -1369, 1369}, {x, -Round[(Abs[31250 - 2z^3]/3)^(1/2)], Round[(Abs[31250 - 2z^3]/3)^(1/2)]}]
%t A336450 u = Union@t;
%t A336450 v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 2739}];
%t A336450 Select[v, MemberQ[u, #] &]
%Y A336450 Cf. A000290, A000578, A003215, A004825, A004826, A047201, A050791, A130472, A195006, A336449.
%K A336450 sign
%O A336450 1,2
%A A336450 _XU Pingya_, Aug 08 2020